In certain mild extensions of the standard model, spin-independent long range forces can arise by exchange of two very light pseudoscalar spin-0 bosons. In particular, we have in mind models in which these bosons do not have direct tree level couplings to ordinary fermions. Using the dispersion theoretical method, we find a 1/r³ behavior of the potential for the exchange of very light pseudoscalars and a 1/r⁷ dependence if the pseudoscalars are true massless Goldstone bosons.
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Ferrer et al. (1999) studied this question.
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